Episode 3: Introduction to just intonation | The Royal Wind Music & Seldom Sene

Episode 3: Introduction to just intonation | The Royal Wind Music & Seldom Sene

This is Maria… and this is Hester!
And together we are the CONSORT COUNSELLORS! Today we are going to speak about tuning,
which is, as you know, one of the most challenging aspects of ensemble playing. We would like to tell you all the secrets to tune the consonances: the unison, the octave, the fifth, the fourth,
the major and the minor third. We all know that two recorder players are better than one.
And why is that…? Because when they play two different pitches together, something magical happens. They create TWO extra notes,
and that is no horror: that is just the laws of physics. You may actually want to grab your headphones
to be able to hear this. Let’s take a sopranino and a garklein… I’m going to play
the middle D and I’m going to keep it really stable. Hester is going to play the middle A on the garklein
and she’s going to start playing very soft, and then she’s going to play louder and louder
so that the pitch rises. Listen out for a very low buzz going around the room. You may have noticed that our playing went from ‘dreadful’
to ‘really steady and stable’. The ‘dreadful’ parts were out of tune
and the ‘stable and steady parts’ were in tune, with the right DIFFERENCE TONES. Why is that?
Well, that is because the difference tone that you’re talking about is your best friend for tuning. But, what is actually the difference tone? The difference tone is called like that because it is the difference between the frequency of the highest pitch that is sounding
MINUS the frequency of the lower pitch. Then you get that lower difference tone. An example: when a sound that vibrates 300 cycles per second
is combined with a sound that vibrates 200 cycles per second you will get a difference tone that vibrates 100 cycles per second. When the difference tone is matching one of the tones that we are playing or is creating a consonance with one of those tones,
the music sounds in tune. Before we move on we would like to give you
one last piece of information, something to listen to. Besides the difference tone, which is a LOW tone, when we play two sounds together we also hear a HIGHER one, on top of the sounds we are producing.
This is called the SUM TONE. We are going to play again and move the pitch around.
Look for something really HIGH buzzing around the room. Now we are ready to check out the intervals we need to make music together. Let’s start with the UNISON,
in which we are both playing exactly the same note, which means also exactly the same frequency. The difference between two equal frequencies is actually… no difference tone! So, when you play a unison really in tune
it sounds very sweet, calm and stable. If the unison is not perfectly well in tune you will notice
that there is a lot of instability going on, because the frequencies of the two pitches are very close together,
so you hear a lot of unstable sounds. Let’s move on to the OCTAVE. When we play an OCTAVE together, the frequency of the lowest tone is exactly half of the frequency of the highest tone. If the frequency of the low pitch is 1, the frequency of the high pitch is 2. For that reason, a recorder that is an octave lower than another,
is also exactly twice the size. Since 2 – 1=1, we hear the difference tone which has
exactly the same pitch I play: the low A. The bottom note is reinforced; therefore the root in an octave
should also sound richer than the upper octave. When we play a perfect FIFTH, the frequency of the lower pitch
is 2/3 of the higher pitch, So: when the lower pitch equals 2 the
higher pitch of a perfect fifths equals 3. Let’s hear that! As Hester said: imagine that ‘her’ tone equals 3 and
my tone equals 2… Then the difference tone is 3-1=1! And … is 1 half of 2, which is my own tone.
So, actually, the difference tone is “my” tone, but an octave lower! When we play a perfect FOURTH, the [frequency of the] lower pitch
is 3/4 of the [frequency of the] higher pitch. Imagine the low pitch is 3
and the perfect fourth on top is 4. Let’s hear that! That was the FOURTH! And you’re probably starting
to get the hang of this: if my frequency is 4 and Hester’s is
3, the difference between those is… 1! That means that when we are playing a fourth,
it’s ‘my tone’, the A – the upper tone – that is reinforced and ‘confirmed’ by the difference tone –
but two octaves lower! When we play a MAJOR THIRD, the frequency of the lowest tone is 4/5 of the frequency of the highest tone. Imagine that Hester’s frequency is 4,
then my frequency will be 5. Hester is going to play an A
and I am going to play a C-sharp, we hear the MAJOR THIRD. And again! 5 –4=1, so ‘my’ pitch, the A. is reinforced! Two octaves lower… Moving on to MINOR THIRDS!
This is an interesting one… When we play a minor third together, the frequency of the lower pitch is 5/6 of the [frequency of] the higher pitch. I’m going to play a high C-sharp
and Maria is going to play an E on top of that. My pitch equals 5 and Maria’s pitch equals 6! You already see it coming, don’t you…?
The difference between 6 and 5 is 1! I played an E, Hester played a C-sharp,
but number 1 in this row of intervals we’ve been tuning… …is the low A!
We create: E + C-sharp + A, which is a major triad. And that is why the difference tone is our best friend!
Our trio partner… At this point, I guess you are all wondering…
OK, but how do we practice this? So we have some exercises for you! One player chooses a pitch that they really like
and play it really stable. Hester is playing an A! I’m going to play a C-sharp
on top of it, which is a MAJOR THIRD! Another possible exercise to practice several intervals is… Hester, could you play a nice low D for me? What I’m going to do is play a melody that I really like,
“Vader Jacob” [Are you sleeping?]! I will play the first eight notes of that melody
starting on a low F, and that will give me minor thirds, fourths and fifths on top of Hester’s note
which I can tune by listening carefully to the difference tones. And I guess we can also improvise a melody then!
María, could you please play an E for me? I’m going to improvise a little ‘medieval melody’
on top of your E. This was our very short introduction
to something that we call JUST INTONATION, which is this way of tuning, based on the natural overtones present on all sounds. Therefore, it is a very pleasant and natural way of tuning.
It is the ‘purest” form of intonation, with all intervals in tune. All the [theoretical] knowledge about just intonation
is very important, but we don’t have time to think when we are actually playing pieces –
like “oh I’m too high, oh, I’m too low…” Actually we should be able to FEEL when we are in tune. In later episodes we will come back to this subject: tuning – so, STAY TUNED! We hope you can excuse us if the 30-seconds tip of today is about us. Of course, not just about us, but
about our consorts the ensembles we play in. We play, for example, with The Royal Wind Music.
This is our latest CD: “Cosmography of Polyphony”. The Royal Wind Music is a very special consort of Renaissance recorders
founded by Paul Leenhouts in 1997. We also play with Seldom Sene Recorder Quintet.
Our latest CD, “Delight in Musicke” just arrived, fresh from the press. On the CD you can find English songs and instrumental music
from the 16th and 17th century. Don’t forget to subscribe
and if you have questions or comments for us, contact us HERE!
See you next time, bye!

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About the Author: Oren Garnes


  1. Hi! Wonderfull idea of making this videos! Thanks. I have just one comment about headphones. Yes, it works on headphones, but only because the mic collected difference tones. From my experience I know, that it works much stronger, when there are really two speakers playing two different tones. So the difference tones are created really in air, not from the speakers. But it means You should record two separate tracks and put one to the right speaker and other to the left. With normal stereo recording those waves are actually recorded by microphone, which is also great of course. Well, anyway it's always great idea to explain it so good as You did. Thanks once more!

  2. I often hear odd or even harmonics in Music, so I know what you are trying to reference, but I didn't hear the "difference tone" in your example. Not at all. I only heard your two Recorders, whether in tune or not
    … nor did I hear a "sum tone". I only heard the "low buzz" very slightly when she first started playing the Sopranino out of tune, and I have a very, very well-trained ear…

  3. Thank you so much for this. As a math/physics nerd, I love to hear about and hear all these tones! One thing I hope you will try (although not idiomatic for Renaissance music) is going beyond fifths and thirds, to take on seconds and sevenths. For example, the minor seventh may be 9:5, 16:9, or 7:4, which sound very different! (and not to mention all the different ways to do the tritone). For example, do you know the old-fashioned American singing tradition of "Barbershop Quartet" with a lot of harmonies using the septimal 7th? Since the recorder is such an excellent instrument for microtonal shadings, I think it is great to explore these harmonies! As the Bass from my college dorm's Quartet, and a recorder player for even longer than that, I throw down the gauntlet. Let's see you do these harmonies! :^) https://www.youtube.com/watch?v=MdTS6-fbNH0

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